INTRODUCTION: WHY WAVELETS?

Wavelets, or more precisely, wavelet transformations, abound in image‐processing applications. The Federal Bureau of Investigation uses wavelets in their Wavelet Scalar Quantization Specification to compress digital images of fingerprints. In this case there is an objective measure of the effectiveness of the compression method ‐ the uncompressed fingerprint file must be uniquely matched with the correct person. In many instances it is desirable to identify edges of regions that appear in digital images. Wavelets have proved to be an effective way to perform edge detection in images. There are several reasons why wavelets work well in many applications. Probably the most important is the fact that a discrete wavelet transformation is a local transformation. The chapter also presents an overview of key concepts covered in this book. The book presents an ad hoc development of wavelet transformations and an introduction to some applications that use them.